from itertools import combinations import time import threading from collections import defaultdict import math from multiprocessing import Pool # 配置参数(优化阈值) TARGET = 65000 # 目标值 BASE_VALUES = [38.5,44,61,70.5,75.5,93] # 基础系数列表 FLUCTUATION = 1.0 # 系数波动范围 MAX_SOLUTIONS = 3 # 每个组合的最大解数量 SOLVER_TIMEOUT = 180 # 求解超时时间(秒) THREE_VAR_THRESHOLD = 259000 # 使用三个变量的阈值 PRODUCT_RANGE_THRESHOLD = 129000 # 乘积范围限制阈值 HIGH_TARGET_THRESHOLD = 259000 # 更高目标值阈值 SHOW_PROGRESS = True # 是否显示进度 MAX_SOLUTIONS_PER_COMB = 100 # 每个组合的最大解数量,用于提前终止 USE_MULTIPROCESSING = True # 是否使用多进程加速 def is_valid_product(p): """确保单个乘积不超过129000""" return p <= 129000 # 严格限制所有乘积不超过129000 def find_single_variable_solutions(values): """查找单个数的解(a*x = TARGET)""" solutions = [] for a in values: quotient = TARGET / a if quotient != int(quotient): continue x = int(quotient) if 1 <= x <= 10000 and is_valid_product(a * x): solutions.append((a, x)) if len(solutions) >= MAX_SOLUTIONS: break return solutions def find_two_variable_solutions(values): """优化的双变量求解算法,确保每个乘积不超过129000""" solutions = defaultdict(list) for i, a in enumerate(values): for b in values[i:]: seen_xy = set() # 调整x的最大值,确保a*x不超过129000 if max_x < min_x: continue x_count = max_x - min_x + 1 x_step = max(1, x_count // 1000) for x in range(min_x, max_x + 1, x_step): ax = a * x if ax > 129000: # 额外检查确保不超过129000 continue remainder = TARGET - ax if remainder < b: break if remainder > b * 10000: continue if remainder % b == 0: y = remainder // b by = b * y if 1 <= y <= 10000 and by <= 129000: # 确保b*y也不超过129000 xy_pair = (x, y) if a <= b else (y, x) if xy_pair not in seen_xy: seen_xy.add(xy_pair) solutions[(a, b)].append((a, x, b, y)) if len(solutions[(a, b)]) >= MAX_SOLUTIONS_PER_COMB: break return solutions def process_three_var_combination(args): """处理三变量组合的辅助函数,用于并行计算""" a, b, c, value_ranges, target = args solutions = [] seen_xyz = set() min_x, max_x = value_ranges[a] x_count = max_x - min_x + 1 x_step = max(1, x_count // 1000) for x in range(min_x, max_x + 1, x_step): ax = a * x if not is_valid_product(ax): continue remainder1 = target - ax if remainder1 < 0: break if max_y < min_y: continue y_count = max_y - min_y + 1 y_step = max(1, y_count // 100) for y in range(min_y, max_y + 1, y_step): by = b * y if not is_valid_product(by): continue remainder2 = remainder1 - by if remainder2 < 0: break if remainder2 > c * 10000: continue if remainder2 % c == 0: z = remainder2 // c if 1 <= z <= 10000 and is_valid_product(c * z): xyz_tuple = tuple(sorted([x, y, z])) if xyz_tuple not in seen_xyz: seen_xyz.add(xyz_tuple) solutions.append((a, x, b, y, c, z)) if len(solutions) >= MAX_SOLUTIONS_PER_COMB: return solutions return solutions def find_three_variable_solutions(values): """优化的三变量求解算法,确保每个乘积不超过129000""" solutions = defaultdict(list) sorted_values = sorted(values) # 预计算每个系数的有效范围,确保每个乘积不超过129000 value_ranges = {} for a in sorted_values: value_ranges[a] = (min_x, max_x) combinations_list = [] for i, a in enumerate(sorted_values): for j in range(i + 1, len(sorted_values)): b = sorted_values[j] for k in range(j + 1, len(sorted_values)): c = sorted_values[k] combinations_list.append((a, b, c, value_ranges, TARGET)) if USE_MULTIPROCESSING: with Pool() as pool: results = pool.map(process_three_var_combination, combinations_list) for i, (a, b, c, _, _) in enumerate(combinations_list): if results[i]: solutions[(a, b, c)] = results[i] else: total_combinations = len(combinations_list) for i, (a, b, c, _, _) in enumerate(combinations_list): res = process_three_var_combination((a, b, c, value_ranges, TARGET)) if res: solutions[(a, b, c)] = res if SHOW_PROGRESS and i % 10 == 0: print(f"\r三变量组合进度: {i}/{total_combinations} 组", end='') if SHOW_PROGRESS and not USE_MULTIPROCESSING: print(f"\r三变量组合进度: {total_combinations}/{total_combinations} 组 - 完成") return solutions def find_balanced_solutions(solutions, var_count, num=2): """从所有解中筛选出最平衡的解""" if var_count == 1 or not solutions: return solutions balanced = [] for sol in solutions: vars = sol[1::2] # 获取解中的变量值 diff = max(vars) - min(vars) # 计算变量之间的最大差值 balanced.append((diff, sol)) # 按差值排序,返回差值最小的解 return [s for _, s in sorted(balanced, key=lambda x: x[0])[:num]] def find_original_solutions(solutions, balanced_solutions, num=3): """从剩余解中获取原始顺序的解""" if not solutions: return [] remaining = [s for s in solutions if s not in balanced_solutions] return remaining[:num] def display_solutions(solutions_dict, var_count): """优化的解显示函数""" if not solutions_dict: return print(f"\n找到 {len(solutions_dict)} 组{var_count}变量解:") for i, (coeffs, pair_solutions) in enumerate(sorted(solutions_dict.items()), 1): balanced = find_balanced_solutions(pair_solutions, var_count) original = find_original_solutions(pair_solutions, balanced) all_display = balanced + original if var_count == 1: a = coeffs print(f"\n{i}. 组合: a={a} ({len(pair_solutions)} 个有效解)") elif var_count == 2: a, b = coeffs print(f"\n{i}. 组合: a={a}, b={b} ({len(pair_solutions)} 个有效解)") else: a, b, c = coeffs print(f"\n{i}. 组合: a={a}, b={b}, c={c} ({len(pair_solutions)} 个有效解)") for j, sol in enumerate(all_display, 1): tag = "[平衡解]" if j <= len(balanced) else "[原始解]" if var_count == 1: a, x = sol print(f" {j}. x={x}, a*x={a*x:.1f}, 总和={a*x:.1f} {tag}") elif var_count == 2: a, x, b, y = sol print(f" {j}. x={x}, y={y}, a*x={a*x:.1f}, b*y={b*y:.1f}, 总和={a*x + b*y:.1f} {tag}") else: a, x, b, y, c, z = sol print(f" {j}. x={x}, y={y}, z={z}, " f"a*x={a*x:.1f}, b*y={b*y:.1f}, c*z={c*z:.1f}, " f"总和={a*x + b*y + c*z:.1f} {tag}") def run_with_timeout(func, args=(), kwargs=None, timeout=SOLVER_TIMEOUT): """运行函数并设置超时限制""" if kwargs is None: kwargs = {} result = [] error = [] def wrapper(): try: result.append(func(*args, **kwargs)) except Exception as e: error.append(e) thread = threading.Thread(target=wrapper) thread.daemon = True thread.start() thread.join(timeout) if thread.is_alive(): print(f"警告: {func.__name__} 超时({timeout}秒),跳过此方法") return None if error: return result[0] def main(): print(f"目标值: {TARGET}") # 生成波动后的系数 FLUCTUATED_VALUES = [round(v - FLUCTUATION, 1) for v in BASE_VALUES] # 尝试基础系数 print(f"\n==== 尝试基础系数 ====") # 目标值255966 > 259000不成立,会按顺序尝试单、双、三变量解 base_solutions = { 'single': run_with_timeout(find_single_variable_solutions, args=(BASE_VALUES,)), 'two': run_with_timeout(find_two_variable_solutions, args=(BASE_VALUES,)), 'three': [] } has_solution = False # 显示单变量解 if base_solutions['single']: has_solution = True display_solutions({a: [sol] for a, sol in zip(BASE_VALUES, base_solutions['single']) if sol}, 1) # 显示双变量解 if base_solutions['two'] and len(base_solutions['two']) > 0: has_solution = True display_solutions(base_solutions['two'], 2) # 单变量和双变量都无解时,尝试三变量解 if not has_solution: print(f"\n==== 单变量和双变量无解,尝试三变量解 ====") base_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(BASE_VALUES,)) if base_solutions['three'] and len(base_solutions['three']) > 0: has_solution = True display_solutions(base_solutions['three'], 3) if has_solution: print(f"\n使用基础系数列表,共找到有效解") return # 如果基础系数没有找到解,尝试波动系数 print(f"\n==== 尝试波动系数 ====") fluctuated_solutions = { 'single': run_with_timeout(find_single_variable_solutions, args=(FLUCTUATED_VALUES,)), 'two': run_with_timeout(find_two_variable_solutions, args=(FLUCTUATED_VALUES,)), 'three': [] } has_solution = False # 显示单变量解 if fluctuated_solutions['single']: has_solution = True display_solutions({a: [sol] for a, sol in zip(FLUCTUATED_VALUES, fluctuated_solutions['single']) if sol}, 1) # 显示双变量解 if fluctuated_solutions['two'] and len(fluctuated_solutions['two']) > 0: has_solution = True display_solutions(fluctuated_solutions['two'], 2) # 单变量和双变量都无解时,尝试三变量解 if not has_solution: print(f"\n==== 单变量和双变量无解,尝试三变量解 ====") fluctuated_solutions['three'] = run_with_timeout(find_three_variable_solutions, args=(FLUCTUATED_VALUES,)) if fluctuated_solutions['three'] and len(fluctuated_solutions['three']) > 0: has_solution = True display_solutions(fluctuated_solutions['three'], 3) if has_solution: print(f"\n使用波动系数列表,共找到有效解") return # 如果所有系数集都没有找到解 print("\n没有找到符合条件的解,即使使用波动后的系数列表。") if __name__ == "__main__": main() print(f"\n总耗时: {time.time() - start_time:.2f}秒")
Standard input is empty
目标值: 65000 ==== 尝试基础系数 ==== 找到 13 组2变量解: 1. 组合: a=38.5, b=61 (14 个有效解) 1. x=622, y=673.0, a*x=23947.0, b*y=41053.0, 总和=65000.0 [平衡解] 2. x=744, y=596.0, a*x=28644.0, b*y=36356.0, 总和=65000.0 [平衡解] 3. x=12, y=1058.0, a*x=462.0, b*y=64538.0, 总和=65000.0 [原始解] 4. x=134, y=981.0, a*x=5159.0, b*y=59841.0, 总和=65000.0 [原始解] 5. x=256, y=904.0, a*x=9856.0, b*y=55144.0, 总和=65000.0 [原始解] 2. 组合: a=38.5, b=70.5 (12 个有效解) 1. x=542, y=626.0, a*x=20867.0, b*y=44133.0, 总和=65000.0 [平衡解] 2. x=683, y=549.0, a*x=26295.5, b*y=38704.5, 总和=65000.0 [平衡解] 3. x=119, y=857.0, a*x=4581.5, b*y=60418.5, 总和=65000.0 [原始解] 4. x=260, y=780.0, a*x=10010.0, b*y=54990.0, 总和=65000.0 [原始解] 5. x=401, y=703.0, a*x=15438.5, b*y=49561.5, 总和=65000.0 [原始解] 3. 组合: a=38.5, b=75.5 (11 个有效解) 1. x=496, y=608.0, a*x=19096.0, b*y=45904.0, 总和=65000.0 [平衡解] 2. x=647, y=531.0, a*x=24909.5, b*y=40090.5, 总和=65000.0 [平衡解] 3. x=43, y=839.0, a*x=1655.5, b*y=63344.5, 总和=65000.0 [原始解] 4. x=194, y=762.0, a*x=7469.0, b*y=57531.0, 总和=65000.0 [原始解] 5. x=345, y=685.0, a*x=13282.5, b*y=51717.5, 总和=65000.0 [原始解] 4. 组合: a=38.5, b=93 (9 个有效解) 1. x=524, y=482.0, a*x=20174.0, b*y=44826.0, 总和=65000.0 [平衡解] 2. x=338, y=559.0, a*x=13013.0, b*y=51987.0, 总和=65000.0 [平衡解] 3. x=152, y=636.0, a*x=5852.0, b*y=59148.0, 总和=65000.0 [原始解] 4. x=710, y=405.0, a*x=27335.0, b*y=37665.0, 总和=65000.0 [原始解] 5. x=896, y=328.0, a*x=34496.0, b*y=30504.0, 总和=65000.0 [原始解] 5. 组合: a=44, b=61 (24 个有效解) 1. x=590, y=640, a*x=25960.0, b*y=39040.0, 总和=65000.0 [平衡解] 2. x=651, y=596, a*x=28644.0, b*y=36356.0, 总和=65000.0 [平衡解] 3. x=41, y=1036, a*x=1804.0, b*y=63196.0, 总和=65000.0 [原始解] 4. x=102, y=992, a*x=4488.0, b*y=60512.0, 总和=65000.0 [原始解] 5. x=163, y=948, a*x=7172.0, b*y=57828.0, 总和=65000.0 [原始解] 6. 组合: a=44, b=70.5 (11 个有效解) 1. x=580, y=560.0, a*x=25520.0, b*y=39480.0, 总和=65000.0 [平衡解] 2. x=439, y=648.0, a*x=19316.0, b*y=45684.0, 总和=65000.0 [平衡解] 3. x=16, y=912.0, a*x=704.0, b*y=64296.0, 总和=65000.0 [原始解] 4. x=157, y=824.0, a*x=6908.0, b*y=58092.0, 总和=65000.0 [原始解] 5. x=298, y=736.0, a*x=13112.0, b*y=51888.0, 总和=65000.0 [原始解] 7. 组合: a=44, b=75.5 (9 个有效解) 1. x=585, y=520.0, a*x=25740.0, b*y=39260.0, 总和=65000.0 [平衡解] 2. x=434, y=608.0, a*x=19096.0, b*y=45904.0, 总和=65000.0 [平衡解] 3. x=132, y=784.0, a*x=5808.0, b*y=59192.0, 总和=65000.0 [原始解] 4. x=283, y=696.0, a*x=12452.0, b*y=52548.0, 总和=65000.0 [原始解] 5. x=736, y=432.0, a*x=32384.0, b*y=32616.0, 总和=65000.0 [原始解] 8. 组合: a=44, b=93 (16 个有效解) 1. x=505, y=460, a*x=22220.0, b*y=42780.0, 总和=65000.0 [平衡解] 2. x=412, y=504, a*x=18128.0, b*y=46872.0, 总和=65000.0 [平衡解] 3. x=40, y=680, a*x=1760.0, b*y=63240.0, 总和=65000.0 [原始解] 4. x=133, y=636, a*x=5852.0, b*y=59148.0, 总和=65000.0 [原始解] 5. x=226, y=592, a*x=9944.0, b*y=55056.0, 总和=65000.0 [原始解] 9. 组合: a=61, b=70.5 (7 个有效解) 1. x=527, y=466.0, a*x=32147.0, b*y=32853.0, 总和=65000.0 [平衡解] 2. x=386, y=588.0, a*x=23546.0, b*y=41454.0, 总和=65000.0 [平衡解] 3. x=104, y=832.0, a*x=6344.0, b*y=58656.0, 总和=65000.0 [原始解] 4. x=245, y=710.0, a*x=14945.0, b*y=50055.0, 总和=65000.0 [原始解] 5. x=668, y=344.0, a*x=40748.0, b*y=24252.0, 总和=65000.0 [原始解] 10. 组合: a=61, b=75.5 (7 个有效解) 1. x=469, y=482.0, a*x=28609.0, b*y=36391.0, 总和=65000.0 [平衡解] 2. x=620, y=360.0, a*x=37820.0, b*y=27180.0, 总和=65000.0 [平衡解] 3. x=16, y=848.0, a*x=976.0, b*y=64024.0, 总和=65000.0 [原始解] 4. x=167, y=726.0, a*x=10187.0, b*y=54813.0, 总和=65000.0 [原始解] 5. x=318, y=604.0, a*x=19398.0, b*y=45602.0, 总和=65000.0 [原始解] 11. 组合: a=61, b=93 (12 个有效解) 1. x=410, y=430, a*x=25010.0, b*y=39990.0, 总和=65000.0 [平衡解] 2. x=503, y=369, a*x=30683.0, b*y=34317.0, 总和=65000.0 [平衡解] 3. x=38, y=674, a*x=2318.0, b*y=62682.0, 总和=65000.0 [原始解] 4. x=131, y=613, a*x=7991.0, b*y=57009.0, 总和=65000.0 [原始解] 5. x=224, y=552, a*x=13664.0, b*y=51336.0, 总和=65000.0 [原始解] 12. 组合: a=70.5, b=75.5 (6 个有效解) 1. x=439, y=451.0, a*x=30949.5, b*y=34050.5, 总和=65000.0 [平衡解] 2. x=590, y=310.0, a*x=41595.0, b*y=23405.0, 总和=65000.0 [平衡解] 3. x=137, y=733.0, a*x=9658.5, b*y=55341.5, 总和=65000.0 [原始解] 4. x=288, y=592.0, a*x=20304.0, b*y=44696.0, 总和=65000.0 [原始解] 5. x=741, y=169.0, a*x=52240.5, b*y=12759.5, 总和=65000.0 [原始解] 13. 组合: a=75.5, b=93 (5 个有效解) 1. x=298, y=457.0, a*x=22499.0, b*y=42501.0, 总和=65000.0 [平衡解] 2. x=484, y=306.0, a*x=36542.0, b*y=28458.0, 总和=65000.0 [平衡解] 3. x=112, y=608.0, a*x=8456.0, b*y=56544.0, 总和=65000.0 [原始解] 4. x=670, y=155.0, a*x=50585.0, b*y=14415.0, 总和=65000.0 [原始解] 5. x=856, y=4.0, a*x=64628.0, b*y=372.0, 总和=65000.0 [原始解] 使用基础系数列表,共找到有效解 总耗时: 0.01秒